Learn Swedish: Hon är den enda som vet. - She is the only one who knows.

In Swedish, den enda translates fully to "the only one". You do not need to add an extra word like en after it. A common mistake for English speakers is trying to say den enda en, but Swedish leaves the extra word out when the meaning is already clear.

Why does the sentence use som instead of vem for "who"?

Vem is strictly a question word used to ask "Who?" (for example, Vem vet? means "Who knows?"). When you are connecting parts of a sentence with "who", "which", or "that", you must use the connecting word som.

How do I know whether to use vet or känner for "knows" here?

Swedish uses vet when you know a fact, a secret, or a piece of information, which fits this sentence perfectly. You only use känner when you are talking about knowing or being familiar with a person or a place.

Would enda change if we were talking about a man instead of a woman?

You can use den enda for anyone. You might occasionally see den ende used specifically for a male in formal writing, but den enda is standard and perfectly correct for both men and women in everyday modern Swedish.